On functions that are approximate fixed points almost everywhere and Ulam’s type stability

Research paper by Anna Bahyrycz, Janusz Brzdęk, Eliza Jabłońska, Jolanta Olko

Indexed on: 07 Jul '15Published on: 07 Jul '15Published in: Journal of Fixed Point Theory and Applications


In this paper, we investigate functions that are approximate fixed points of some (possibly nonlinear) operators almost everywhere, with respect to some ideals of sets. We prove that (under suitable assumptions) there exist fixed points of the operators that are “near” those functions. The results are applied to obtain some general stability results of Ulam’s type almost everywhere; in particular, for the polynomial functional equation.